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In a recent PRL Barci and Stariolo (BS) generalized the well known Brazovskiimodel to include an additional rotationally invariant quartic interaction andstudy this model in two dimensions (2d). Depending on the parameters of themodel, BS find two transitions: a first order isotropic-lamellar (striped) or asecond order isotropic-nematic (which they speculate to be in theKosterlitz-Thouless universality class). Using a simple symmetry argument, Ishow that the striped phase found by BS can not exist in 2d. Furthermore, Iargue that based on the coarse-grained action used by BS it is impossible toreach any conclusion about the nature of the isotropic-nematic transition.

physical review letters

Comment on: Competing Interactions, the Renormalization Group, and the  Isotropic-Nematic Phase Transition, by D. Barci and D. Stariolo, Phys. Rev.  Lett. 98, 200604 (2007)